Chaos signatures in the short and long time behavior of the out-of-time ordered correlator

Understand

Two properties are needed for a classical system to be chaotic: exponential stretching and mixing.

• Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of physical systems.
• While most of the attention has previously been devoted to the short time stretching aspect of chaos, characterized by the Lyapunov exponent, we show for quantum maps that the out-of-time correlator approaches its stationary value exponentially with a rate determined by the Ruelle-Pollicot resonances.
• This property constitutes clear evidence of the dual role of the underlying classical chaos dictating the behavior of the correlator at different timescales.